Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For an IVP $y' = f(x,y)$, with initial condition $y(x_0) = \alpha$, can something be said about how large the error at $x_1$, $x_1 > x_0$, is going to be if instead we had started with the initial condition $y(x_0) = \alpha + h$ for a small $h$? Of course, I'm assuming both solutions guaranteed by the Existence-Uniqueness theorem extend to $x_1$.

share|cite|improve this question
up vote 3 down vote accepted

Yes, one can say pretty much (assuming enough regularity). The buzzword is "dependence on the initial value" and you may have a look at this for example.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.